Which of the following represents a geometric sequence?

Mathematics

1 answer:

Leto [7]3 years ago

6 0

The answer is A

1/4, 1/4, 1/4, 1,4...

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One light-year equals 5.9 x 1012 miles. How many light-years are in 6.79

inna [77]

Option B

The number of light years in $6.79 \times 10^{16}$ miles is 11508 light years

Solution:

Given that,

One light-year equals 5.9 x 10^12 miles

Therefore,

$1 \text{ light year } = 5.9 \times 10^{12} \text{ miles }$

To find: Number of light years in $6.79 \times 10^{16}$ miles

Let "x" be the number of light years in $6.79 \times 10^{16}$ miles

Then number of light years in $6.79 \times 10^{16}$ miles can be found by dividing $6.79 \times 10^{16}$ miles by miles in 1 light year

$\text{Number of light years in } 6.79 \times 10^{16} miles = \frac{6.79 \times 10^{16}}{5.9 \times 10^{12}}\\\\\text{Use the law of exponent }\\\\\frac{a^m}{a^n} = a^{m-n}\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = \frac{6.79}{5.9} \times 10^{16-12}\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = 1.1508 \times 10^4\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = 11508$